Dimension-Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse

TL;DR

This paper investigates how the critical exponent in spherically symmetric scalar field gravitational collapse varies with spacetime dimensions from 3.5 to 14, revealing a monotonic increase towards an asymptotic value.

Contribution

It provides the first detailed analysis of the dimension dependence of the critical exponent in scalar collapse beyond four dimensions.

Findings

Critical exponent increases with dimension D

Asymptotic value of the exponent is approximately 0.466

Exponent fits an exponential growth model with respect to D

Abstract

We study the critical behaviour of spherically symmetric scalar field collapse to black holes in spacetime dimensions other than four. We obtain reliable values for the scaling exponent in the supercritical region for dimensions in the range $3.5\leq D\leq 14$. The critical exponent increases monotonically to an asymptotic value at large $D$ of $\gamma\sim0.466$. The data is well fit by a simple exponential of the form: $\gamma \sim 0.466(1-e^{-0.408 D})$.